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This brief introduces readers to various problems in cancer biology that are amenable to analysis using methods of probability theory and statistics, building on only a basic background in these two topics.   Aside from providing a self-contained introduction to several aspects of basic biology and to cancer, as well as to the techniques from statistics most commonly used in cancer biology, the brief describes several methods for inferring gene interaction networks from expression data, including one that is reported for the first time in the brief.  The application of these methods is illustrated on actual data from cancer cell lines.  Some promising directions for new research are also discussed.   After reading the brief, engineers and mathematicians should be able to collaborate fruitfully with their biologist colleagues on a wide variety of problems.

Cancer -- Computer simulation. --- Cancer -- Mathematical models. --- Computational biology. --- Computational biology --- Cancer --- Models, Theoretical --- Diseases --- Statistics as Topic --- Regulatory Sequences, Nucleic Acid --- Biology --- Epidemiologic Methods --- Health Care Evaluation Mechanisms --- Biological Science Disciplines --- Investigative Techniques --- Base Sequence --- Public Health --- Natural Science Disciplines --- Analytical, Diagnostic and Therapeutic Techniques and Equipment --- Genetic Structures --- Quality of Health Care --- Health Care Quality, Access, and Evaluation --- Genetic Phenomena --- Disciplines and Occupations --- Environment and Public Health --- Phenomena and Processes --- Health Care --- Neoplasms --- Models, Statistical --- Gene Regulatory Networks --- Computational Biology --- Health & Biological Sciences --- Biology - General --- Computer simulation --- Mathematical models --- Data processing. --- Cancers --- Carcinoma --- Malignancy (Cancer) --- Malignant tumors --- Computer science. --- Cancer research. --- Bioinformatics. --- Systems biology. --- Biomathematics. --- Statistics. --- Control engineering. --- Computer Science. --- Computational Biology/Bioinformatics. --- Physiological, Cellular and Medical Topics. --- Control. --- Statistics for Life Sciences, Medicine, Health Sciences. --- Systems Biology. --- Cancer Research. --- Bioinformatics --- Tumors --- Physiology --- Biological models. --- Oncology. --- Control and Systems Theory. --- Mathematics. --- Models, Biological --- Statistical analysis --- Statistical data --- Statistical methods --- Statistical science --- Mathematics --- Econometrics --- Animal physiology --- Animals --- Anatomy --- Bio-informatics --- Biological informatics --- Information science --- Systems biology --- Data processing --- Statistics . --- Cancer research --- Biological systems --- Molecular biology --- Control engineering --- Control equipment --- Control theory --- Engineering instruments --- Automation --- Programmable controllers

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519.71 --- Factorization (Mathematics) --- #TELE:SISTA --- Mathematics --- 519.71 Control systems theory: mathematical aspects --- Control systems theory: mathematical aspects --- Control theory --- Dynamics --- Machine theory --- Control theory. --- Factorization (Mathematics).

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This book introduces the so-called ""stable factorization approach"" to the synthesis of feedback controllers for linear control systems. The key to this approach is to view the multi-input, multi-output (MIMO) plant for which one wishes to design a controller as a matrix over the fraction field F associated with a commutative ring with identity, denoted by R, which also has no divisors of zero. In this setting, the set of single-input, single-output (SISO) stable control systems is precisely the ring R, while the set of stable MIMO control systems is the set of matrices whose elements all belong to R. The set of unstable, meaning not necessarily stable, control systems is then taken to be the field of fractions F associated with R in the SISO case, and the set of matrices with elements in F in the MIMO case. The central notion introduced in the book is that, in most situations of practical interest, every matrix P whose elements belong to F can be ""factored"" as a ""ratio"" of two matrices N,D whose elements belong to R, in such a way that N,D are coprime. In the familiar case where the ring R corresponds to the set of bounded-input, bounded-output (BIBO)-stable rational transfer functions, coprimeness is equivalent to two functions not having any common zeros in the closed right half-plane including infinity. However, the notion of coprimeness extends readily to discrete-time systems, distributed-parameter systems in both the continuous- as well as discrete-time domains, and to multi-dimensional systems. Thus the stable factorization approach enables one to capture all these situations within a common framework. The key result in the stable factorization approach is the parametrization of all controllers that stabilize a given plant. It is shown that the set of all stabilizing controllers can be parametrized by a single parameter R, whose elements all belong to R. Moreover, every transfer matrix in the closed-loop system is an affine function of the design parameter R. Thus problems of reliable stabilization, disturbance rejection, robust stabilization etc. can all be formulated in terms of choosing an appropriate R. This is a reprint of the book Control System Synthesis: A Factorization Approach originally published by M.I.T. Press in 1985. Table of Contents: Filtering and Sensitivity Minimization / Robustness / Extensions to General Settings.

Data mining. --- Statistics. --- Data Mining and Knowledge Discovery.

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System analysis. --- Differential equations, Nonlinear.

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